Abstract: Despite being a well understood phenomenon in the context of current terrestrial experiments, neutrino flavor conversions in dense astrophysical environments probably represent one of the most challenging open problems in neutrino physics. Apart from being theoretically interesting, such a problem has several phenomenological implications in cosmology and in astrophysics, including the primordial nucleosynthesis of light elements abundance and other cosmological observables, nucleosynthesis of heavy nuclei, and the explosion of massive stars. In this review, we briefly summarize the state of the art on this topic, focusing on three environments: early Universe, core-collapse supernovae, and compact binary mergers.

Abstract: Neutrino non-standard interactions (NSI) with electrons are known to alter the picture of neutrino de coupling from the cosmic plasma. NSI modify both flavour oscillations through matter effects, and the annihilation and scattering between neutrinos and electrons and positrons in the thermal plasma. In view of the forthcoming cosmological observations, we perform a precision study of the impact of non universal and flavour-changing NSI on the effective number of neutrinos, Neff. We present the variation of Neff arising from the different NSI parameters and discuss the existing degeneracies among them, from cosmology alone and in relation to the current bounds from terrestrial experiments. Even though cosmology is generally less sensitive to NSI than these experiments, we find that future cosmological data would provide competitive and complementary constraints for some of the couplings and their combinations.

Abstract: The ordering of the neutrino masses is a crucial input for a deep understanding of flavor physics, and its determination may provide the key to establish the relationship among the lepton masses and mixings and their analogous properties in the quark sector. The extraction of the neutrino mass ordering is a data-driven field expected to evolve very rapidly in the next decade. In this review, we both analyse the present status and describe the physics of subsequent prospects. Firstly, the different current available tools to measure the neutrino mass ordering are described. Namely, reactor, long-baseline (accelerator and atmospheric) neutrino beams, laboratory searches for beta and neutrinoless double beta decays and observations of the cosmic background radiation and the large scale structure of the universe are carefully reviewed. Secondly, the results from an up-to-date comprehensive global fit are reported: the Bayesian analysis to the 2018 publicly available oscillation and cosmological data sets provides strong evidence for the normal neutrino mass ordering vs. the inverted scenario, with a significance of 3.5 standard deviations. This preference for the normal neutrino mass ordering is mostly due to neutrino oscillation measurements. Finally, we shall also emphasize the future perspectives for unveiling the neutrinomass ordering. In this regard, apart from describing the expectations from the aforementioned probes, we also focus on those arising from alternative and novel methods, as 21 cm cosmology, core-collapse supernova neutrinos and the direct detection of relic neutrinos.

Abstract: When neutrino masses arise from the exchange of neutral heavy leptons, as in most seesaw schemes, the effective lepton mixing matrix N describing neutrino propagation is non-unitary, hence neutrinos are not exactly orthonormal. New CP violation phases appear in N that could be confused with the standard phase delta(CP) characterizing the three neutrino paradigm. We study the potential of the long-baseline neutrino experiment DUNE in probing CP violation induced by the standard CP phase in the presence of non-unitarity. In order to accomplish this we develop our previous formalism, so as to take into account the neutrino interactions with the medium, important in long baseline experiments such as DUNE. We find that the expected CP sensitivity of DUNE is somewhat degraded with respect to that characterizing the standard unitary case. However the effect is weaker than might have been expected thanks mainly to the wide neutrino beam. We also investigate the sensitivity of DUNE to the parameters characterizing non-unitarity. In this case we find that there is no improvement expected with respect to the current situation, unless the near detector setup is revamped.

Abstract: Current neutrino experiments are measuring the neutrino mixing parameters with an unprecedented accuracy. The upcoming generation of neutrino experiments will be sensitive to subdominant neutrino oscillation effects that can in principle give information on the yet-unknown neutrino parameters: the Dirac CP-violating phase in the PMNS mixing matrix, the neutrino mass ordering and the octant of.23. Determining the exact values of neutrino mass and mixing parameters is crucial to test various neutrino models and flavor symmetries that are designed to predict these neutrino parameters. In the first part of this review, we summarize the current status of the neutrino oscillation parameter determination. We consider the most recent data from all solar neutrino experiments and the atmospheric neutrino data from Super-Kamiokande, IceCube, and ANTARES. We also implement the data from the reactor neutrino experiments KamLAND, Daya Bay, RENO, and Double Chooz as well as the long baseline neutrino data from MINOS, T2K, and NO.A. If in addition to the standard interactions, neutrinos have subdominant yet-unknown Non-Standard Interactions (NSI) with matter fields, extracting the values of these parameters will suffer from new degeneracies and ambiguities. We review such effects and formulate the conditions on the NSI parameters under which the precision measurement of neutrino oscillation parameters can be distorted. Like standard weak interactions, the non-standard interaction can be categorized into two groups: Charged Current (CC) NSI and Neutral Current (NC) NSI. Our focus will bemainly on neutral current NSI because it is possible to build a class of models that give rise to sizeable NC NSI with discernible effects on neutrino oscillation. These models are based on new U(1) gauge symmetry with a gauge boson of mass. 10 MeV. The UV complete model should be of course electroweak invariant which in general implies that along with neutrinos, charged fermions also acquire new interactions on which there are strong bounds. We enumerate the bounds that already exist on the electroweak symmetric models and demonstrate that it is possible to build viable models avoiding all these bounds. In the end, we review methods to test these models and suggest approaches to break the degeneracies in deriving neutrino mass parameters caused by NSI.